arXiv subjects
Publications and source records attributed to A. Politi.
A coupled-map lattice showing complex behavior in presence of a fully negative Lyapunov spectrum is considered. A phase transition from ordered to disordered evolution upon changing diffusive coupling is studied in detail. Various indicators provide a coherent description of the scenario: the existence of an intermediate transition region characterized by an irregular alternancy of periodic and chaotic evolution.
We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed.
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is derived on the basis of this relationship. An approximate expression for the nonlinear velocity is also determined by extending the concept of Lyapunov exponent to growth rate of finite perturbations.